Using some of the world's most advanced photoelectron spectroscopy and
computing techniques, Berkeley Lab scientists gained a more precise understanding
of the electrical properties of fullerenes, those famous soccer-ball-shaped
molecules comprised of 60 carbon atoms.

The team, which also includes researchers from Stanford University and
Europe, obtained the first experimental measurement of the range of energies
possessed by electrons, as a function of their momenta, in a single layer
of carbon-60 molecules doped with additional electrons, a step that transforms
the molecule into one of the best known superconductors, meaning it conducts
electricity without resistance below a certain critical temperature.

Buckyballs are soccer ball-shaped
60-atom clusters of pure carbon.

As expected in a molecular solid, they found that the electrons' energy-momentum
range, also called the bandwidth, is quite narrow. But they were surprised
by how narrow. And when they compared their measurements to theoretical
calculations, they determined why.

"We knew the bandwidth was small. But our research reveals, experimentally,
that it's even smaller than anticipated," says Steven Louie, a theoretical
physicist in Berkeley Lab's Materials Sciences Division and a professor
of physics at the University of California at Berkeley. "And we determined
that the additional 50-percent reduction is consistent with the effects
of electron-phonon interactions."

Their work, reported in the April 11, 2003, issue of Science,
demonstrates how the electronic properties of fullerenes and similar molecules
are affected by interactions between electrons and phonons — particles
associated with atomic vibrations in a solid. This, in turn, will inform
further research on other fullerene properties such as heat capacity and
electron transport, possibly laying the groundwork for real-world applications.

A new form of carbon

Discovered in 1985 during experiments on carbon clusters using atomic
beams, carbon-60 was named buckminsterfullerene, or buckyball, because
it resembles American architect R. Buckminster Fuller's geodesic domes.
Since then scientists have engineered giant fullerenes with as many as
960 carbon atoms, "buckybabies" with 32 atoms, and elongated
structures such as nanotubes.

The molecules join diamond and graphite as the only forms of pure carbon,
and have been heralded as stars in the burgeoning field of nanoscience,
with potential uses as lubricants, drug delivery agents, and superconductors.
In particular, researchers remain intrigued over the latter: when a carbon-60
solid is doped by inserting alkali atoms such as potassium into empty
spaces within its crystal structure, it becomes superconducting at the
relatively high temperature of about 40 degrees Kelvin. Because most conventional
superconductors require temperatures at or below 20 degrees Kelvin, doped
fullerenes offer a potentially easier way to incorporate zero resistance
into electrical systems. Only the high-Tc cuprate superconductors have
higher transition temperatures.

More research is needed however. Topping the to-do list is a precise
measurement of the molecular solid's bandwidth. In other words, what is
the energy-momentum range of the electrons, from the most tightly bound
to the least tightly bound, in a given band? And what factors dictate
this range? Based on theoretical calculations (and some indirect experimental
evidence) conducted in the 18 years since its discovery, scientists know
doped fullerene solids have a narrow bandwidth, and they know this is
most likely due to interactions between electrons and phonons. But these
theories lacked definitive experimental support.

To obtain this support, the team used Berkeley Lab's Advanced Light Source
(ALS), a synchrotron that emits light in the x-ray region of the electromagnetic
spectrum that is one billion times brighter than the sun. They subjected
a doped carbon-60 monolayer to these extremely bright x-rays, which bombard
the sample with photons. Electrons in the fullerene layer absorb the photons,
gain energy, and bounce out of the layer. A detector then records the
electrons' kinetic energies, which indicates the energy level they occupied
in the layer. After recording a range of these electrons, the team produced
the first photoemission measurement of a doped fullerene layer's bandwidth
and band dispersion, which is the relationship between electron energy
versus momentum.

Like running through water

This experimental bandwidth mirrored bandwidths derived from theoretical
calculations, except for one important detail. It was 50 percent narrower.
This means the electrons observed in the sample possessed less kinetic
energy for a given momentum than expected. Or, put another way, they appeared
to have more mass. The Berkeley Lab team knew this was an illusion; the
electrons don’t possess more mass. Rather, the ALS data captured
an interaction between electrons and some other particle that dulls the
electrons’ energy-momentum and makes them appear heavier —
much like a person trying to run in water will accelerate much more slowly,
and seem to have more mass, than when they run on land.

But what acts like water in this case? What particle impairs the electrons’
energy-momentum? Earlier research pointed to one of two culprits: either
electron-electron interactions, or electron-phonon interactions. The former
phenomenon is easily explained. Because they repel one another, electron
interactions make electrons appear heavier.

Phonons, however, are more difficult to grasp. Just as light can behave
like a wave, as in an electromagnetic wave, or like a particle, as in
a photon, so too can atomic vibrations that reverberate through a crystal
structure. In classical physics, vibrations behave like sound waves, but
at the quantum level, vibrations become particles called phonons. They’re
created and absorbed as electrons push through the crystal lattice and
distort the position of surrounding atoms. These distortions make the
electrons appear heavier for a given momentum, the same way a person moves
slower and feels heavier when attempting to run through water.

To determine if this phenomenon is responsible for the ALS experiment’s
heavier-than-expected electrons, and narrowed bandwidth, the team turned
to quantum mechanical calculations conducted at Berkeley Lab’s National
Energy Research Scientific Computing Center (NERSC). There, they calculated
the bandwidth and band dispersion of the carbon-60 monolayer using purely
theoretical principles. They then compared the theoretical bandwidth,
with and without electron-phonon effects, to the ALS-produced bandwidth,
and got a nearly perfect match.

“It all falls together,” Louie says. “This experiment
shows, at least for a monolayer on top of a metallic surface, that we
don’t need additional phenomena like electron-electron interactions
to explain the bandwidth. It also provides a quantitative understanding
of the importance of electron-phonon interactions.”

The research is described in the Science paper, “Band Structure
and Fermi Surface of Electron-Doped C60 Monolayers.” In addition
to Louie, Berkeley Lab researchers Wan Li Yang and Zahid Hussain of the
ALS, and Hyoungjoon Choi and Marvin Cohen of the Materials Sciences Division,
contributed to the research. Other collaborators include Z. -X. Shen from
Stanford University, and scientists from France’s Paris-Sud University,
Italy’s Trieste Synchrotron, and Italy’s University Cattolica
del Sacro Cuore.